Such an electrical impedance tomography device (EIT device) is known, for example, from EP 1 000 580 A1, which is used to record an “electrical impedance tomogram” of the cross section of the thorax of a patient.
Electrical impedance tomography is a method for the reconstruction of impedance distributions, more precisely impedance changes relative to a reference distribution, in electrically conductive bodies. A plurality of electrodes are placed for this on the surface of the body to be examined. A ring-shaped equidistance array of 16 electrodes, which can be placed around the thorax of a patient with a belt, is used in typical cases.
The control and analysis unit has analog electrical circuits for signal amplification and for feeding alternating current and electronic circuits for digitizing and preprocessing the voltage signals as well as a digital signal processor for controlling the device and for processing the recorded data for reconstructing the impedance distribution. The control and analysis unit ensures that one pair each of (preferably) adjacent electrodes is supplied with an alternating electric current (e.g., 5 mA at 50 kHz) and the electric voltages are detected on a plurality of remaining electrode pairs by the control and analysis unit (it is also possible, in principle, conversely to feed an alternating voltage to an electrode pair and to measure the alternating currents over a plurality of remaining electrode pairs); the voltages of all remaining pairs of adjacent electrodes are typically detected, but it is also possible, in principle, to skip individual electrodes, as a result of which information will, however, be lost. The impedance distribution, more precisely, the change in the impedance distribution compared to a reference distribution (e.g., the impedance distribution during the first recording), can be reconstructed with algorithms from the totality of all measured signals during the consecutive current feeds, during which the position of the feeding electrode pair migrates around the electrode ring step by step. The prior-art algorithms yield as the result of the reconstruction a matrix of 32×32 image elements, and the matrix contains for each image element the reconstructed impedance change for this image element. A plurality of such matrices are recorded at preset time intervals during at least one inhalation and at least one exhalation, e.g., over one breath with inhalation and an exhalation following it. These are displayed on a display device consecutively, as a result of which the intratidal time course of the impedance change is made visible practically as a film.
Thoracic electrical impedance tomography for measuring the regional lung ventilation has been increasingly used in intensive care medicine focused on research. Theoretical models and experimental comparisons of EIT with CT images of the thorax show a nearly complete proportionality of the air content in the lung tissue and the impedance of the latter. The breaths are resolved spatially with about 20% of the thoracic diameter and in time typically with about 20 to about 40 matrices per second, which makes possible a bed-side monitoring of the regional lung ventilation. The matrices are occasionally also called images of the impedance distribution (with 32×32=1024 image elements) or frames.
Consequently, a sequence of impedance changes, which is also called here a time series of impedance change values for the given image element, is determined for each image element over one phase of inhalation or one phase of exhalation. The terms time series of impedance change values and impedance change curves will hereinafter be used synonymously, even though a time series comprising discrete points is not a curve in the strict sense of the word. The time series are also represented in the form of curves as functions of time in the diagrams for reasons of representation.
An essential advantage of the high frame rate is that the breaths, especially the phase of inhalation and the phase of exhalation of the breath, can be resolved over time. Therefore, it is possible not only to analyze not only the regional distribution of the ventilated air in the end-inspiratory state (tidal image), but also to investigate the course over time during the inhalation and exhalation in order to infer regional lung mechanical processes therefrom. For example, the behavior of the local impedance change curves is thus examined compared to the global impedance change curve in the article “New Methods for Improving the Imaging Quality in Functional EIT Tomograms of the Lungs,” G. Kühnel et al., Biomed. Tech. (Berlin), 42 (1997), Suppl. 470-1, but the difference in behavior during inhalation and exhalation was not taken into account, but a “filling capacity,” which is a variable related to the tidal image, was determined from the slope of a fitted straight line (this would have to be explained somewhat more accurately). Local inhalation curves are determined in the article “Regional Ventilation Delay Index: Detection of Tidal Recruitment Using Electric Impedance Tomography,” T. Muders et al., Vincent J. L., ed., Yearbook of Intensive Care and Emergency Medicine, and the time at which the local inhalation curve reaches 40% of its maximum is related to the global inhalation time for each local inhalation curve, and an image of faster or slower regions with lower or higher time constants than the average is generated from this. A “regional ventilation delay index (RVD)” is defined from this as an indicator of the inhomogeneity over time.
However, none of the methods simultaneously takes into account the inhalation curve and the exhalation curve and consequently nor the amount of work of breathing dissipated at the alveolar level. The work of breathing at the alveolar level is almost completely stored in the ideal case elastically by the expansion of the alveoli and of the thorax during the inhalation and the stored energy is released again passively during the exhalation. There is no hysteresis in this case between inhalation and exhalation. This is true, of course, at the alveolar level only. If the normal breathing pressure is measured at the mouthpiece or at the upper bronchi, a hysteresis is obtained already because of the volume-dependent frictional losses of the air flow in the airways. These can be estimated and calculated by fitting the data to motion equations of breathing mechanical models.
A simple breathing mechanical model in mechanical ventilation, in which the lungs are considered to be a compartment with frictional resistance of the flexible tube and of the airways R and with the system compliance C, ignoring losses due to inertia and turbulence as well as the diaphragmatic pressure, leads to the motion equation:
            p      0        ⁡          (      t      )        =                              R          ⁡                      (            V            )                          ⁢                              d            ⁢                                                  ⁢            V                                d            ⁢                                                  ⁢            t                              +                        V          ⁡                      (            t            )                                    C          ⁡                      (            p            )                                =                            p          R                ⁡                  (          t          )                    +                                    p            dv                    ⁡                      (            t            )                          .            Here, V(t) is the respirated air volume and p0(t) is the upper airway pressure. The first term pR(t) is the pressure drop due to friction at the airways, while the second term palv(t) can be interpreted as the mean alveolar pressure (mean alveolar pressure means here averaged over all alveoli, and this mean alveolar pressure over the breath is a function of time).
In healthy lungs, the compliance C can be assumed to be constant, i.e., independent from the pressure in case of small differences in pressures between inhalation and exhalation. Thus, the volume is linearly dependent in this model on the mean alveolar pressure palv(t), which is, in turn, proportional to the global impedance change (the sum of all local impedance changes of the individual image elements is called the global impedance change here). Therefore, there should not be any hysteresis between the alveolar pressure palv(t) and the volume curve V(t) and hence relative to the global impedance change curve Zglo(t) (however, there is a hysteresis, in general, between the volume V(t) and the airway pressure p0(t)).
In case of spatially and temporally homogeneous lungs, this should also be true of the local impedance change curves (i.e., the impedance change in a pixel in the image plane), i.e., there should not be any hysteresis between the mean alveolar pressure palv(t) and the local impedance change curves. If, however, some of the alveoli no longer work in the purely elastic range, an alveolar p-V hysteresis will develop there.